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刘中宪, 梁建文, 赵瑞斌. 流体饱和层状半空间中沉积谷地对地震波的散射— IBIEM求解[J]. 岩土工程学报, 2013, 35(3): 512-522.
引用本文: 刘中宪, 梁建文, 赵瑞斌. 流体饱和层状半空间中沉积谷地对地震波的散射— IBIEM求解[J]. 岩土工程学报, 2013, 35(3): 512-522.
LIU Zhong-xian, LIANG Jian-wen, ZHAO Rui-bin. Indirect boundary integral equation method for solving scattering of seismic waves by an alluvial valley in fluid poroelastic layered half-space[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(3): 512-522.
Citation: LIU Zhong-xian, LIANG Jian-wen, ZHAO Rui-bin. Indirect boundary integral equation method for solving scattering of seismic waves by an alluvial valley in fluid poroelastic layered half-space[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(3): 512-522.

流体饱和层状半空间中沉积谷地对地震波的散射— IBIEM求解

Indirect boundary integral equation method for solving scattering of seismic waves by an alluvial valley in fluid poroelastic layered half-space

  • 摘要: 针对流体饱和层状半空间中任意形状沉积谷地对地震波的散射问题,基于单层位势理论,建立一种新的间接边界积分方程法(IBIEM):首先推导饱和层状半空间中两类膨胀波源和剪切波源动力格林函数,进而由分布在沉积谷地和层状半空间交界面附近两虚拟波源面上的PI、PII和SV波源分别构造沉积内外的散射波场。由交界面连续性条件建立方程并求解确定虚拟波源密度,总波场即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较,验证了方法的计算精度。通过一组典型算例,初步探讨了平面SV波在饱和层状半空间中沉积谷地周围散射的基本规律。研究表明:饱和层状沉积对地震波的散射和相应干土情况存在显著差异,边界渗透条件对沉积内部地震响应具有重要影响;饱和层状场地中波的散射和均质半空间情况有着本质不同,总体反应体现了饱和土层的共振放大效应和沉积谷地对波的散射效应。实际场地中地震波传播的精确模拟需考虑岩土介质的多相性和层理特征。

     

    Abstract: A new indirect boundary integral equation method for numerically solving the scattering of seismic waves by a two-dimensional alluvial valley of arbitrary shape in poroelastic layered half-space is proposed based on the single layer potential approach. The Green's functions of compressional and shear wave sources in poroelastic layered half-space are derived firstly, then the scattered waves in alluvial valley and layered half-space are constructed by using the fictitious wave sources close to the interface between the valley and the half-space respectively, and the magnitude of the fictitious wave sources is determined through continuous boundary conditions, and the total response can be obtained by the superposition of the free field and the scattered field. The precision of the proposed method is verified by the satisfaction extent of boundary conditions and the comparison between the degenerated solutions of single-phased half-space and the well-known solutions. The diffraction of plane SV waves around an alluvial valley in poroelastic layered half-space is studied with a typical example. It is illustrated that there exists significant difference between the scattering of waves around the poroelastic alluvial valley and the dry soil valley, and the drainage condition has large impact on earthquake ground motion in the valley. The wave scattering in layered sites and that in homogenous half-space are different in nature, and the total response characteristics combine the resonant behavior of the soil layers and the characteristics of scattering waves around the alluvial valley. Hence, to simulate the propagation of seismic waves more accurately, it is necessary to consider the multi-phased and layered characteristics of soil medium in reality.

     

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